a controllability index for heat exchanger networks

A Controllability Index for Heat Exchanger Networks

Denis L. Westphalen,† Brent R. Young, and William Y. Svrcek*

Department of Chemical and Petroleum Engineering, University of Calgary,2500 University Drive NW, Calgary, AB, Canada T2N 1N4

Heat exchanger networks are widely employed in the chemical processing industries to recoverenergy, resulting in reduced operating costs. Several methodologies can be found in the literaturefor the optimal design of heat exchanger networks. Typical optimal criteria are maximum energyrecovery and minimum heat-transfer area. However, the heat integration of process streamscan lead to process structures that are difficult to control. In this work, a heat exchanger networkcontrollability index is proposed as a measure of heat exchanger network controllability. Thiscontrollability index can be calculated easily, making it quite appropriate for use at the conceptualdesign stage of a chemical process. A case study is presented in which the controllability indexis used to compare the controllability characteristics of different networks and also to identifythe tradeoffs between controllability and heat integration.

1. Introduction

The design of heat exchanger networks (HENs) is asubject that has received significant attention duringthe past 3 decades. Furman and Sahinidis1 publisheda detailed review of the literature on heat exchangernetwork synthesis and cited some 460 articles. HENsynthesis is not only an important research area, as theliterature presents an extensive list of examples inwhich new design methodologies have been successfullyapplied in actual industrial cases. In plain words, thesynthesis of an HEN can be described as the design ofthe heat exchangers for a given process in which allprocess hot and cold streams reach their specified outlettemperatures, using minimum annualized investmentand operating costs as the performance criteria.

The heat integration of process streams can lead toprocess structures that are difficult to control, and insome cases, this inhibits retrofit of existing processes.Luyben et al.2 presented a general procedure for plant-wide control, for the case in which energy integrationdramatically alters the dynamic behavior of the plant.In this situation, special attention must be paid to theprocess-to-process heat exchangers, particularly if theyare used for heat removal from exothermic reactors.Controllability is an important issue that should betaken into account in HEN synthesis.

Kotjabasakis and Linnhoff3 introduced the concept ofsensitivity tables and described how heat exchangerareas should be increased with the aim of increasingthe network’s flexibility. Their method is intuitive andis particularly useful when there is a need to improvethe controllability of an existing HEN. However, it isnot possible to incorporate the issue of flexibility duringthe topological conception of the network.

Investigating the process control of HENs, Mathisenet al.4 proposed some heuristic rules for bypass place-ment and the selection of manipulated variables. Glem-mestad et al.5-7 proposed a method for the optimal

operation of HENs, whereby the process is periodicallyoptimized to define new set points for some key tem-peratures.

However, better operation can be achieved usingsimple control structures.

Oliveira et al.8 analyzed in detail the interactionsbetween the process control and design of a particularHEN, using steady-state optimization and the calcula-tion of the condition number for the selection of ma-nipulated variables. No information on the dynamicbehavior was used in their problem formulation, andas a result, the designed network had poor controllabil-ity. In summary, the bulk of the literature is concernedwith the problem of the process control of existingnetworks, that is, networks that have already beendesigned, and as a consequence, the proposed method-ologies cannot be used at the synthesis stage.

The use of a resilience index (RI)9-12 has beenproposed as a measurement of flexibility, operability,and controllability of a given process. Some attemptshave been made to use an RI in the design of HENs.The resulting methodology generates HENs that canhandle inlet temperature variations. Because onlyenergy balances are used in the calculations and noconsideration is given to heat-transfer areas, the resultsof this methodology are not useable.

The goal of this work is to present a new controllabil-ity index for HENs. This index is intended to be aprimary function of the network’s topology that does notdepend on a particular control strategy or set of ma-nipulated variables. It must be easily calculated so thatit can be used as a conceptual design tool. It is expectedthat the use of this controllability index will enableprocess engineers to include process control issues atan early stage, namely, conceptual design.

2. Process Control of Heat Exchanger Networks

An HEN is typically employed to perform heat ex-change, so that each process stream attains its specifiedtemperature. Every process is subjected to randomdisturbances and operator upsets, which necessitates aprocess control scheme that will keep all outlet temper-atures near their set-point values. As a first step,

* To whom correspondence should be addressed. E-mail:[email protected].

† Present address: Aspen Technology, Calgary, AB, Canada.

4659Ind. Eng. Chem. Res. 2003, 42, 4659-4667

10.1021/ie020893z CCC: $25.00 © 2003 American Chemical SocietyPublished on Web 07/30/2003

strategies for the control of individual heat exchangersare discussed below, and then strategies for the controlof networks are analyzed.

2.1. Process-to-Utility Heat Exchangers. Process-to-utility heat exchangers are defined as those heatexchange operations that exchange heat between aprocess stream and a utility stream, as shown in Figure1. The outlet temperature of the process stream can beeasily controlled using the flow rate of the utility streamas the manipulated variable (e.g., Svrcek et al.13 andDriedger14). Generally, the utility system of a chemicalcomplex is designed to absorb large disturbances in theprocess, making process-to-utility heat exchangers rela-tively easy to control.

2.2. Process-to-Process Heat Exchangers. Process-to-process heat exchangers are defined as those heatexchange operations that exchange heat between twoprocess streams, as shown in Figure 2. The outlettemperature of one process stream can be controlledusing the bypass flow of the other stream as themanipulated variable. During the operation of a heat

exchanger, if the bypass flow rate is increased, the meantemperature difference is reduced, resulting in a smallerduty, as exemplified in Figure 3 (where calculationswere performed using a constant UA value). As a result,the “actual” manipulated variable is the heat load of theheat exchanger. For that reason, it is not possible tocontrol both outlet temperatures in the same heatexchanger, e.g., using bypass streams on both sides.Furthermore, a process-to-process heat exchanger thatwill be used to control an outlet temperature must bedesigned with a nonzero bypass flow rate to handledisturbances that require an increase or decrease of theheat load. Because the existence of a bypass streamresults in smaller mean temperature differences, largerareas must be employed, resulting in larger capitalcosts. Steady-state simulations show that, from aneconomic point of view, the bypass stream should beplaced on the stream with the largest heat flow rate

Figure 1. Process control of process-to-utility heat exchangers:(A) use of cold utility, (B) use of hot utility.

Figure 2. Process control of process-to-process heat exchangers.

Figure 3. Influence of bypass stream on temperature differ-ences: (A) 0% bypass flow ratio, (B) 20% bypass flow ratio.

Figure 4. Heat exchanger network from stream data shown inTable 1.

4660 Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003

capacity, because this stream can handle larger distur-bances with less additional capital cost, when comparedto the situation in which the bypass is placed on thestream with the smallest heat flow rate capacity. Seborget al.15 stated that manipulated variables that “rapidly”affect the controlled variables should be selected. Usingthis principle, dynamic simulations indicate that thebypass stream must be placed on the exchanger streamthat has its outlet temperature controlled, indepen-dently of the heat flow rate capacity values. Steady-stateand dynamic simulations can lead to conflicting conclu-sions, and as a general principle, dynamic results shouldbe used in the design of control schemes.

2.3. Heat Exchanger Networks. HENs contain bothprocess-to-utility and process-to-process heat exchang-ers. Stream splitting is commonly employed in HENs,and as explained by Westphalen et al.,16 stream divisionin a stream splitter should not be used as a manipulatedvariable in an HEN because it might not affect thedownstream outlet temperatures monotonically.

Figure 4 shows an HEN with four process streamsand six heat exchangers in a grid diagram. Table 1presents the stream data for this network. If all fouroutlet stream temperatures are controlled, then fourmanipulated variables should be selected. Each heatexchanger can contribute one manipulated variable (itsheat load), resulting in the selection of four heat

exchangers. Westphalen el al16 proposed some heuristicrules for the selection of heat exchangers for processcontrol. Methodologies4,5,8,16 for the selection of themanipulated variables in an HEN are well-documentedand are not discussed in this paper.

3. Relative Gain Array and Heat ExchangerNetworks

The relative gain array (RGA) is a tool that iscommonly used to determine the pairings of controlled/manipulated variables in a control scheme, more specif-ically, eliminating the bad pairings. The first step inthe calculation of the RGA is the calculation of thesteady-state process gains (Kij). These gain values showhow a specific manipulated variable affects a controlledvariable. For instance, a bypass stream can be placed

Figure 5. Graphical user interface of the software tool developed in this work.

Table 1. Stream Data

stream

inlettemperature

(°C)

supplytemperature

(°C)

mean flowrate capacity

(kW/K)

H1 170.0 60.0 30.0H2 150.0 30.0 15.0C1 20.0 135.0 20.0C2 80.0 140.0 40.0

Table 2. RGAs for All Possible Combinations ofManipulated Variables

set manipulated variables identity matrix

1 E1, E2, E3, E4 no2 E1, E2, E3, E5 yes3 E1, E2, E3, E6 yes4 E1, E2, E4, E5 yes5 E1, E2, E4, E6 yes6 E1, E2, E5, E6 no7 E1, E3, E4, E5 no8 E1, E3, E4, E6 no9 E1, E3, E5, E6 yes10 E1, E4, E5, E6 yes11 E2, E3, E4, E5 yes12 E2, E3, E4, E6 yes13 E2, E3, E5, E6 a14 E2, E4, E5, E6 a15 E3, E4, E5, E6 yes

a Gain matrix is singular.

Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 4661

on the cold side of heat exchanger E2. If the bypass ratioon heat exchanger E2 (Figure 4) is increased from 0.1(nominal value) to 0.2 and all other manipulatedvariables are kept constant, then the steady-state outlettemperatures of streams H1, H2, C1, and C2 will changeto 66.7, 22.9, 130.4, and 140.0 °C, respectively. Thesteady-state process gain is calculated as the ratio ofthe change in a controlled variable to that in a manipu-lated variable. Thus, from the above results, the follow-ing process gains can be calculated

The same procedure could be repeated for the otherheat exchangers assuming a specific position (hot or coldside) of the bypass streams for each process-to-processheat exchanger. Because each process-to-process heatexchanger presents two possible placements for thebypass stream, the total number of alternative Kmatrices that could be calculated is 8 (23). However,although the position of the bypass stream will affectthe dynamic behavior of the network, the interactionsshown by the RGA will not change. Because the actualmanipulated variable in each heat exchanger is theduty, the process gain matrix (K) can be calculated byintroducing the step change in the duty instead of inthe bypass stream flow rate. Using this procedure, thefollowing process gain matrix can be calculated for a-10% change in the duty of each heat exchanger

From the gain values, one can conclude that heatexchangers E4, E5, and E6 affect only streams C2, C1,and H2, respectively, and that their loads should beused as manipulated variables to control the outlettemperatures of those streams. Any change to heatexchanger E1 is propagated through the whole network,affecting all outlet temperatures. Therefore, heat ex-changer E1’s duty should not be used as a manipulatedvariable in this network. The process gains help inelucidating process interactions, and in some complexnetworks, it is impossible to interpret all of the interac-tions just by inspection.

The RGA (Λ) is calculated from the process gainmatrix (K) using eq 1, where the symbol × means anelement-by-element multiplication

The interpretation of the elements (λij) of the RGA iswell-described in the literature (e.g., Ogunnaike andRay,17 Svrcek et al.13), and it can be summarized asfollows:

1. For λij ) 1.0, there is no interaction with othercontrol loops, and the pairing i-j should be used.

2. For λij ) 0, manipulated variable j has no effect oncontrolled variable i.

3. For λij ) 0.5, there is a high degree of interactionwith other control loops.

4. For 0.5 < λij < 1.0, there is interaction with othercontrol loops; however, the i-j pairing would be prefer-able as it would minimize interactions.

5. For λij > 1.0, the interaction with other loopsreduces the effect of the control loop.

6. For λij < 0.0, the pairing i-j might lead to anunstable operation.

Because the RGA can be calculated only for a squareprocess gain matrix, the selection of manipulated vari-ables is performed a priori, and the RGA indicates thebest possible pairing. For instance, the use of heatexchangers E3, E4, E5, and E6 results in the followingRGA

Obviously, heat exchangers E3, E4, E5, and E6 shouldbe used to control the outlet temperatures of streamsH1, C2, C1, and H2, respectively. This conclusion canalso be achieved by inspection or by using the heuristicrules presented in the literature.

If, for instance, heat exchangers E2, E4, E5, and E6are selected as manipulated variables, the following gainmatrix is obtained

Given this gain matrix, it is not possible to calculatethe RGA because the gain matrix is singular, andtherefore, no useable pairings exist. Upon furtheranalysis of the network, it can be seen that no heatexchanger affects stream H1; that is, it is impossible tocontrol all outlet temperatures using this choice ofmanipulated variables. It can also be seen that allelements in the RGA corresponding to stream H1 areequal to zero, meaning that no manipulated variableaffects this controlled variable.

A computer program was developed to calculate theRGA of an HEN and implement following algorithm:

KH1,E2 ) 67, KH2,E2 ) -71,KC1,E2 ) -46, KC2,E2 ) 0

K )

E1 E2 E3 E4 E5 E6

[-0.0167 0 -0.0333 0 0 0-0.0179 -0.0667 0.0357 0 0 -0.0667-0.0116 0.0500 0.0232 0 0.0500 0

0.0250 0 0 0.0250 0 0]H1H2C1C2

Λ ) [K-1]T × K (1)

Λ )

E3 E4 E5 E6

[ 1 0 0 00 0 0 10 0 1 00 1 0 0

]H1H2C1C2

K )

E2 E4 E5 E6

[ 0 0 0 0-0.0667 0 0 -0.0667

0.0500 0 0.0500 00 0.0250 0 0

]H1H2C1C2

(1) Define the HEN(stream data, utility data, and topology).

(2) Solve the material, energy, andheat-transfer equations of the network.

(3) Store all results(duties, areas, and outlet temperatures)

for the base case.


The following assumptions were made in the HENmodel: (1) The heat flow rate capacities for all processstreams are constant. (2) Individual heat-transfer coef-ficients are constant for all process and utility streams.(3) Only countercurrent or 1-2 shells are selected. (4)Each heat exchanger can consist of many shells inseries. (5) Heat-transfer equations are solved includingthe FT correction factor.

A “nonsequential equation” solver was developedwhereby each individual process-to-process heat ex-changer can have its duty or area specified. In somecases, where all of the areas of the heat exchangers ina loop are specified, it is not possible to solve theequations of the network. For those cases, the solverautomatically selects the set of heat exchangers that willbe used in an iterative procedure. Figure 5 shows ascreen shot of the output of the program, which waswritten in C++.

Although the RGA is an important tool in the selec-tion of the best manipulated/controlled variable pair-ings, it provides no guidance in the selection of the bestset of manipulated variables. The number of differentpossible combinations of manipulated variables in anetwork can be calculated using

For instance, for the HEN shown in Figure 4, thereare four process streams and six heat exchangers,resulting in a total of 15 possible combinations. TheRGAs were calculated for all 15 combinations, and Table2 shows the combinations that resulted in the RGAbeing similar to the identity matrix, I (containing only0’s and 1’s). Nine different sets of “perfect pairings” areshown; however, there is no information on the controlperformance of each set of these pairings.

4. Condition Number and Heat ExchangerNetworks

As shown in Table 2, for a typical HEN, severaldifferent control schemes can be selected that yield

acceptable controllability. As an additional step, it is ofinterest to compare these different acceptable controlschemes in a quick and reliable way. Furthermore, thecontrollability characteristics of the different networksshould be compared, so that control performance canbe included in the design of new networks in the earlydesign stage.

Ogunnaike and Ray17 suggested that the conditionnumber of the process gain matrix could be used as adimensionless measure of controllability. The conditionnumber of a matrix A is defined as the ratio of thelargest of the wj’s to the smallest of the wj’s, where thewj’s are obtained using a technique called singular valuedecomposition. A matrix is singular if its conditionnumber is infinite, and it is ill-conditioned if its condi-tion number is very large.18

Several case studies were performed, and they showedthat, indeed, the condition number provides an excellentmeasure of controllability for HENs. For the testedconfigurations, the smallest condition numbers alwaysresulted in the most controllable process (from commonsense point of view and dynamic simulations) andcorresponded to relative gain arrays that were close tothe identity matrix.

Table 3 shows the condition numbers for all possiblecombinations of manipulated variables in the networkshown in Figure 4. The largest condition number isobtained when heat exchangers E2, E4, E5, and E6 areselected as the manipulated variables. As discussedearlier, this combination of manipulated variables can-not be used because it does not allow for the simulta-neous control of all outlet temperatures. It can be seenthat the condition numbers of sets 7, 9, 11, and 15 areof the same order of magnitude; therefore, any of themcould be selected for the control scheme. Dynamicsimulation should be used to select the best controlscheme.

5. Controllability Index

The condition number appears to be a useful measureof controllability; that is, it could be used as a control-lability index (CI) to compare different HENs. However,the condition number suffers from the fact that differentvalues can be obtained for the same network (eq 2),depending on the choice of manipulated variables. Froma conceptual design point of view, each new HEN shouldbe designed using the best control scheme. Hence, theCI of an HEN is defined as the smallest of the conditionnumbers obtained for all possible combinations ofmanipulated variables.

(4) Calculate the K matrix:

(4.1) Select a heat exchanger j(process-to-process or process-to-utility).

(4.2) Specify its duty as 90% of the nominal value.

(4.3) Solve the equations of the networkkeeping the areas of all other process-to-

process heat exchangers and the duties ofall other process-to-utility heat exchangers

constant and equal to the values used in thebase case.

(4.4) Calculate all Kij values for heat exchanger j.

(4.5) Repeat steps 4.1-4.4 until all heatexchangers have been selected.

(5) Calculate the RGA:

(5.1) Select a set of manipulated variables.

(5.2) Calculate K-1.

(5.3) Calculate [K-1]T.

(5.4) Calculate the RGA using eq 1.

C ) m!n!(m - n)!

(2)

Table 3. Condition Numbers of All Combinations ofManipulated Variables

set manipulated variables condition number

1 E1, E2, E3, E4 5.52 E1, E2, E3, E5 6.93 E1, E2, E3, E6 8.14 E1, E2, E4, E5 8.65 E1, E2, E4, E6 9.86 E1, E2, E5, E6 1.8 × 1016

7 E1, E3, E4, E5 4.28 E1, E3, E4, E6 6.69 E1, E3, E5, E6 4.810 E1, E4, E5, E6 6.411 E2, E3, E4, E5 4.512 E2, E3, E4, E6 5.313 E2, E3, E5, E6 2.5 × 1023

14 E2, E4, E5, E6 1.0 × 1050

15 E3, E4, E5, E6 3.2


Another important issue in the controllability analysisof HENs is the identification of subnetworks. A subnet-work is defined as an independent set of streams thatare heat-integrated. Figure 6 shows an HEN in whichfour different subnetworks can be identified. Becausethe heat exchangers of one particular subnetwork cannever be selected to pair with an outlet temperature ofa stream located in a different subnetwork, the RGAand condition number should be calculated for eachsubnetwork separately. As proposed previously, the CIof each subnetwork is calculated as the smallest of thecondition numbers obtained for all possible combina-tions of manipulated variables. If, in a given network,all but one subnetwork show good controllability (smallcondition numbers), the subnetwork with poor control-lability impacts the control performance of the wholeHEN, and therefore, the CI of the whole network is

defined as the largest of the CIs obtained for allsubnetworks.

A computer program that calculates the CI of an HENwas developed, and its calculation steps can be sum-marized as follows:

Figure 6. Example of a network with four independent subnetworks (A, B, C, and D).

(1) Define the HEN(stream data, utility data, and topology).

(2) Calculate the gain matrix.

(3) Identify all subnetworks.

(4) For each subnetwork

(4.1) Identify all combinations of manipulatedvariables.


As an example, Table 4 presents the stream data fora refinery crude column preheat train consisting of 19streams. The heat-transfer coefficients for all processstreams were specified as 0.4 kW/(m2 °C). Table 5 showsthe specifications of the process-to-utility heat exchang-

ers, and Table 6 shows the specifications of the process-to-process heat exchangers (1-2 shells) of the networkpresented in Figure 7.

The results are summarized in Table 7. It is possibleto construct 1, 495, 1, 1, and 1 different combinationsof manipulated variables for the subnetworks 1-5,respectively. The condition numbers of subnetworks 1and 3-5 (each of which has only one possible combina-tion) are 8.2, 2.8, 9.6, and 3.2, respectively. However,the smallest condition number of subnetwork 2 (495possible configurations) is 60. According to the proposedmethodology, then, the CI of the network shown inFigure 7 is 60. This large number would suggest thatonly poor controllability can be achieved for this HENand that other topologies should be investigated toimprove the overall controllability of the HEN. Note thatless than 2 s was required to calculate the CI of thisnetwork using a Pentium II 500-MHz PC.

Figure 7. Refinery crude column preheat train.

(4.2) Obtain the calculated gain values anddefine a new gain matrix for the

combination of manipulated variables.

(4.3) Calculate the condition number ofthis new gain matrix.

(4.4) Calculate the CI of the subnetwork as thesmallest of the condition numbers obtained

for all combinations of manipulated variables.

(5) Calculate the CI of the network as thelargest of the CIs obtained for all subnetworks.


6. Case Study

Table 8 shows stream data for a process with two hotand two cold process streams. One network was de-signed using the pinch design method (Figure 8, net-work A), and a different network was designed usingthe “Recommended Designs” feature (an MINLP method)of the software HX-Net19,20 (Figure 9, network B).

Tables 9 and 10 summarize the results of the control-lability analyses performed on networks A and B,respectively. The resulting CIs are 3.95 and 2.50 for

networks A and B, respectively. Therefore, from aprocess controllability point of view, network B ispreferred.

The results in Table 10 suggest that a more thoroughanalysis of the problem is warranted. It can be seen thatthe CI of subnetwork 1 is 2.00; however, the overallcontrollability of the whole network is due to thesubnetwork 2. The heat load of heat exchanger E3 isvery small when compared with the loads of the otherheat exchangers. For that reason, this heat exchangercannot handle the large disturbances in the remainderof network, and the overall controllability could beimproved if this heat exchanger were designed with a


stream

inlettemperature

(°C)

supplytemperature

(°C)


(kW/K)

H1 361.1 252.5 151.9H2 292.0 251.7 637.1H3 288.6 214.9 405.8H4 279.8 54.9 99.7H5 251.7 181.2 100.3H6 221.5 160.5 302.8H7 221.1 91.6 49.7H8 204.9 55.0 101.6H9 168.1 43.9 21.5H12 139.8 41.9 57.4H13 136.5 43.0 51.2H14 120.0 77.6 638.9C1 136.1 348.9 803.6C2 140.0 175.1 69.4C3 140.1 149.6 331.2C4 140.0 149.5 330.5C5 15.0 143.2 298.1C6 15.0 143.1 298.3C10 50.0 105.0 58.3

Table 5. Process-to-Utility Heat Exchangers

unit duty (kW) utility type

E18 98 910 fired heatE19 1586 cold waterE20 800 cold waterE21 4000 cold waterE22 6930 cold waterE23 8230 cold water

Table 6. Process-to-Process Heat Exchangers

unit area (m2) unit area (m2) unit area (m2)

E1 1048.10 E7 173.50 E13 549.17E2 1609.64 E8 414.46 E14 549.17E3 601.99 E9 1258.24 E15 415.66E4 260.93 E10 2531.95 E16 349.14E5 1033.69 E11 268.08 E17 290.21E6 1644.79 E12 756.34

Table 7. Controllability Index Results

subnetwork streamsnumber of

combinations CI

1 H1, C1, H3, H2 1 8.22 H12, C5, H14, C6, H9, H4 495 603 H13, C10 1 9.64 H5, C4, C3 1 9.65 H7, C2 1 3.2


stream

inlettemperature

(°C)

supplytemperature

(°C)


(kW/K)

H1 300.0 80.0 30.0H2 300.0 71.1 45.0C1 40.0 180.0 40.0C2 140.0 240.0 60.0

Figure 8. Case study, network A.

Figure 9. Case study, network B.

Table 9. Controllability Analysis of Network A

setmanipulated

variablesconditionnumber

RGA similarto I?

1 E1, E2, E3, E4 24.1 no2 E1, E2, E3, E5 10.3 no3 E1, E2, E3, E6 4.05 yes4 E1, E2, E4, E5 142 yes5 E1, E2, E4, E6 12.6 no6 E1, E2, E5, E6 5.01 yes7 E1, E3, E4, E5 13.0 no8 E1, E3, E4, E6 3.95 no9 E1, E3, E5, E6 5.71 no10 E1, E4, E5, E6 7.97 no11 E2, E3, E4, E5 14.4 yes12 E2, E3, E4, E6 14.1 no13 E2, E3, E5, E6 7.36 yes14 E2, E4, E5, E6 9.04 yes15 E3, E4, E5, E6 6.23 × 1014 no

Table 10. Controllability Analysis of Network B

setmanipulated

variablesconditionnumber

RGA similarto I?

subnetwork 11 E1, E2 2.00 yes2 E1, E5 2.62 yes3 E2, E5 4.27 yes

subnetwork 21 E3, E4 2.50 yes


larger duty, resulting in less heat integration. Thissimple example shows that a tradeoff between energysavings and controllability is the issue and that it canbe resolved easily using the tools proposed in this work.

7. Conclusions

In this work, a new HEN controllability index, basedon the condition number, is proposed as a measure ofheat exchanger network controllability. This control-lability index can be calculated easily, making it ap-propriate for use during conceptual design and duringplant revamps.

Operating and capital costs are the usual variablesused in the selection of the most suitable HEN for aprocess. Sometimes, the resulting networks are difficultto operate because process control aspects were nottaken into account during the design stage. Moreover,several networks might present comparable costs, andthe controllability index proposed in this work could beused as an additional decision variable.

For a given network, the controllability index providesinsight into ways in which the controllability can beimproved and clearly identifies the tradeoffs being madebetween control performance and energy savings.

This methodology also analyzes all possible pairingsbetween manipulated and controlled variables in anHEN and suggests the best alternatives. The finalsynthesis of the control structure should be checked withthe aid of dynamic simulation tools.

Nomenclature

C ) number of combinationsCI ) controllability indexi ) index for the controlled variable (outlet temperature)j ) index for the manipulated variable (heat exchanger

duty)K ) steady-state process gain matrixKij ) individual element of the process gain matrixm ) number of heat exchangers in the networkn ) number of process streams in the networkΛ ) relative gain array (RGA)λij ) individual element of the relative gain array

Acknowledgment

Financial support from The Pacific Institute for theMathematical Sciences (PIMS), Hyprotech Ltd., and theDepartment of Chemical and Petroleum Engineering isgratefully acknowledged. Dr. Hiren Shethna of Hypro-tech Ltd. is thanked for fruitful discussions.

Literature Cited

(1) Furman, K. C.; Sahinidis, N. V. A Critical Review andAnnotated Bibliography for Heat Exchanger Network Synthesisin the 20th Century. Ind. Eng. Chem. Res. 2002, 41, 2335.

(2) Luyben, M. L.; Tyreus, B. D.; Luyben, W. L. PlantwideControl Design Procedure. AIChE J. 1997, 43, 3161.

(3) Kotjabasakis, E.; Linnhoff, B. Sensitivity Tables for theDesign of Flexible Processes. (1) How Much Contingency in HeatExchanger Networks is Cost-Effective. Chem. Eng. Res. 1986, 64,199.

(4) Mathisen, K. W.; Skogestad, S.; Wolff, E. A. Bypass Selec-tion for Control of Heat Exchanger Networks. Presented at theFirst European Symposium on Computer Aided Process Engineer-ingsESCAPE 1, Elsinore, Denmark, May 24-28, 1992.

(5) Glemmestad, B.; Mathisen, K. W.; Gundersen, T. OptimalOperation of Heat Exchanger Networks Based on StructuralInformation. Comput. Chem. Eng. 1996, 20, S823.

(6) Glemmestad, B.; Gundersen, T. A Systematic Procedure forOptimal Operations of Heat Exchanger Networks. AIChE Symp.Ser. 1998, 320, 94.

(7) Glemmestad, B.; Skogestad, S.; Gundersen, T. OptimalOperation of Heat Exchanger Networks, Comput. Chem. Eng.1999, 23, 509.

(8) Oliveira, S. G.; Liporace, F. S.; Araujo, O. Q. F.; Queiroz,E. M. The Importance of Control Considerations for Heat Ex-changer Network Synthesis: A Case Study. Braz. J. Chem. Eng.2001, 18, 195.

(9) Lenhoff, A. M.; Morari, M. Design of Resilient ProcessingPlants I. Process Design under Consideration of Dynamic Aspects.Chem. Eng. Sci. 1982, 37, 245.

(10) Marselle, D. F.; Morari, M.; Rudd, D. F. Design of ResilientProcessing Plants II. Design and Control of Energy ManagementSystems. Chem. Eng. Sci. 1982, 37, 259.

(11) Saboo, A. K.; Morari, M. Design of Resilient ProcessingPlants IV. Some New Results on Heat Exchanger NetworkSynthesis. Chem. Eng. Sci. 1984, 39, 579.

(12) Saboo, A. K.; Morari, M.; Woodcock, D. C. Design ofResilient Processing Plants VIII. A Resilience Index for HeatExchanger Networks. Chem. Eng. Sci. 1985, 40, 1553.

(13) Svrcek, W. Y.; Mahoney, D. P.; Young, B. R. A Real-TimeApproach to Process Control; John Wiley & Sons Ltd.: Chichester,U.K., 2000.

(14) Driedger, W. Controlling shell and tube exchangers.Hydrocarbon Process. 1998, 77.

(15) Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. ProcessDynamics and Control; John Wiley & Sons: New York, 1989.

(16) Westphalen, D. L.; Young, B. R.; Svrcek, W. Y. Strategiesfor the Operation and Control of Heat Exchanger Networks.Accepted for presentation at the Foundations of Computer-AidedProcess Operations, Coral Springs, FL, 2003.

(17) Ogunnaike, B. A.; Ray, W. H. Process Dynamics, Modelingand Control; Oxford University Press: New York, 1994.

(18) Press: W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling,W. T. Numerical Recipes in CsThe Art of Scientific Computing;Cambridge University Press: Cambridge, U.K., 1988.

(19) HX-Net, version 5.0; Hyprotech Ltd., AEA TechnologyEngineering Software: Calgary, Alberta, Canada, 2001.

(20) Shethna, H. K.; Jezowski, J. M.; Castillo, F. J. L. A NewMethodology for Simultaneous Optimization of Capital and Op-erating Cost Targets in Heat Exchanger Network Synthesis. Appl.Therm. Eng. 2000, 20, 1577.

Received for review November 11, 2002Revised manuscript received May 28, 2003

Accepted May 29, 2003

IE020893Z


a controllability index for heat exchanger networks

Documents